Math 226B: Symplectic GeometryWednesdays 1-2:50pm and Fridays 1-1:50pm
Location: MS 6201
This is a first
course in symplectic geometry. Symplectic geometry is
the study of manifolds equipped with a closed nondegenerate
2-form, called a Instructor: Ko Honda Office: MS 7919Office Hours: TBAE-mail: honda
at math dot ucla dot edu.URL: http://www.math.ucla.edu/~honda
Topics- Basic notions, Darboux's theorem, local normal forms
- Some constructions
- J-holomorphic curves
- Applications, e.g., symplectic capacities
- Sheaves and symplectic geometry
Prerequisites - Math 225A, B, C or equivalent (a good
knowledge of differentiable manifolds and homology).
**Math 226****A is not a prerequisite****for Math 226B.**
Grading
- Based on attendance. If you want an A+,
submit your stack of HW at the end of the quarter.
References- D. McDuff and D. Salamon, Introduction to symplectic topology, 2nd edition, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1998.
- R. Bryant,
*An introduction to Lie groups and symplectic g**eometry*, lecture notes from the Regional Geometry Institute in Park City, Utah, June 24-July 20, 1991. - A. Cannas da Silva,
*Lectures on symplectic geometry,*Lecture Notes in Mathematics 1764, Springer-Verlag, 2008.
- D. McDuff and D. Salamon,
*J-holomorphic curves and symplectic topology,**2nd edition,*American Mathematical Society Colloquium Publications, 52. American Mathematical Society, Providence, RI, 2012.
WARNING: The course syllabus provides a general plan for the course; deviations may become necessary. Last modified: March 7, 2022 |